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PCT, Spin and Statistics, and All That, by Raymond F. Streater, Arthur S. Wightman
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PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.
- Sales Rank: #657643 in Books
- Brand: Brand: Princeton University Press
- Published on: 2000-12-15
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .51" w x 6.00" l, .60 pounds
- Binding: Paperback
- 210 pages
- Used Book in Good Condition
About the Author
Raymond F. Streater is Professor of Applied Mathematics at King's College London. Arthur S. Wightman is Professor Emeritus of Mathematics at Princeton University.
Most helpful customer reviews
15 of 23 people found the following review helpful.
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By Paul J. Werbos
This book is as important to modern physics as Aquinas is to modern religion. And, unlike Aquinas, it has an important Appendix trying to give some flavor of alternative views of the fundamentals.
As Neri notes: the book is widely cited as THE definitive source on the spin-statistics relation, which is more important to practical, real quantum field theory (QFT) than heuristic concepts like the uncertainty principle; yet the proof of spin-statistics and PCT rests on four famous axioms (chapter 3) which do not really make sense in a strict sense, and call out for a proof on a more solid basis.
The book begins (like Aquinas) with some very laudable and lofty goals, such as (1) creation of a completely transparently
relativistic formulation of QFT, unlike the more plodding and earthly and empirically oriented treatments (such as Mandl's text on QFT, which I strongly recommend for those who would want to be more grounded in empirical reality) of "an earlier age"; (2)field operators which represent actual "dressed" particles instead of those pesky "bare fields" that older texts start with. But theer are problems here.
He gives examples in chapter 1 showing that he envisions the wave functions in the new clean theory as objects over what some would call "F4", the Fock space in which N particles are represented by (3+1)*N space-time coordinates, unlike the usual plodding world of F3, of 3*N space coordinates. This is beautiful -- but for physically meaningful local wave packets,
and the usual inner product, these objects do not have finite norms. They do not form a Hilbert space. To assume BOTH this concept of relativistic transformation AND Hilbert space at the same time (the seminal axioms)appears to be a contradiction. At the least, a proper treatment should epxlain what is going on here. Presumably, the later authors (described in the appendix)
who claim that some simple QFTs obey the axioms must have found an operational version or reinterpretation of what the "standard Wightman axioms" mean, but there is no hint of what that could be in the book. I would guess that people have
politely gone back to F3 when analyzing actual theories -- and
are right to do so. But the axioms that are ACTUALLY used when
working in F3 need highlighting.
Also, as other reviewers have noted, "dressed" field operators do not normally have strictly local commutation relations. There goes another one.
Again, the new Appendix is one of the most important parts of the book -- but, as the authors note, it is a bit condensed.
There are many empiricist or postmodernist or new age critics of this book who totally disregard the book for totally wrong reasons. In effect, they say that the quest for a mathematically well-defined theory is itself an unnecessary bore. Some of them might say the same about mathematics itself.
If this book is like Aquinas, those folks are like the creationist thumpers. Yes, there are problems here in the mathematical foundations, but that is no excuse for not trying to fix them. And it is no excuse for totally ignoring the lessons learned in earlier efforts. This book has its problems, but it is better than treatments like those of TV preachers who try to make people feel good by soothing their nerves and their
perceptions, and try to make them feel like guilty sinners whenever a hint of questions enter their minds. Classical
perturbation theory, like the sharia of the Abbasids, has limits which can be truly crippling, no matter how elegantly it is dressed up.
But perhaps we do need a fresh look at what we can figure out in a more plodding logical kind of way, starting from what we
can grasp from empirically-oriented treatments like Mandl's,
or like Walls and Milburn or HJ Carmichael.
23 of 26 people found the following review helpful.
What is a quantum field ?
By henrique fleming
This advanced book exposes the mathematical framework of quantum field theory, as discovered by Wightman, who explained, in an article published in Physics Today, that he was led to such abstract language in order to understand the forces that bind the deuteron nucleus! This was only the beginning: present books and papers on the structure of quantum fields employ (and develop!) mathematics which make the Streater-Wightman book look like Harry Potter. Still, this book is assumed reading for all these advanced studies. It is extremely well written, for one thing. The initial chapter introduces the concept of free particle along ideas which I think belong to Wigner: particles are irreducible representations of the Poicare group. So, group theory is necessary for the grammar of quantum field theory. Fields require Schwartz distribution theory, as intuitively discovered by Bohr and Rosenfeld. Then follow general theorems for local field theory, like spin-statistics, CPT (and all that...). There is now an appendix where more modern topics are presented, but the core of the book is more or less what I described. This is a great book, written with great care and wit. It is a pity that most physicists, even quantum field theorists, did'nt read it.
0 of 0 people found the following review helpful.
Five Stars
By T. Schumann
An excellent book but not easy reading for me. probably my failing not the book's.
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